x=x^2-5x-8

Solution for x=x^2-5x-8 equation:

x=x^2-5x-8

We move all terms to the left:

x-(x^2-5x-8)=0

We get rid of parentheses

-x^2+x+5x+8=0

We add all the numbers together, and all the variables

-1x^2+6x+8=0

a = -1; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-1)·8
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*-1}=\frac{-6-2\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*-1}=\frac{-6+2\sqrt{17}}{-2}
$